abstract algebra help

Show that if the field is generated over by the elements , where each is not algebraic over , then an automorphism of fixing is uniquely determined by . In particular, show that an automorphism fixes if and only if it fixes a set of generators for .

I think I need to define , but I'm not sure how to do it. Can anyone help?

Show that if the field is generated over by the elements , where eachis not algebraic over, then an automorphism of fixing is uniquely determined by . In particular, show that an automorphism fixes if and only if it fixes a set of generators for .

I think I need to define , but I'm not sure how to do it. Can anyone help?

are you sure the assumption is not that "the set is algebraically independent over ?" this is very different from "each being transcendental (= not algebraic) over ."